Our MHD setup requires additional, similar prescriptions for the other quantities
necessary to fully fix both the Parker spiral and the passive tracers
tracking the mixing of material into the gas nebula.
We introduce, in the same fashion as done for the hydrodynamical case
of [1]}, prescriptions for the toroidal and poloidal
components of the stellar surface magnetic field. They read,
\(B_{\star }(r_{\rm in},t) = \Bigg \lbrace \begin{array}{lll}B_{\star }^{\rm bsg} & \mathrm {if} & t \le t_{\rm wr}-\Delta t , \\B_{\star }^{\rm bsg} + \Delta B_{\star }F & \mathrm {if} & t_{\rm wr}-\Delta t < t and t \le t_{\rm wr}, \\B_{\star }^{\rm wr} & \mathrm {if} & t_{\rm wr} < t, \\\end{array}\) 
